Autocorrelation

Computing the cross-correlation of a signal with itself is a mathematical tool for finding repeating patterns in the time-series. Basically we compute the correlation coefficient between the raw data and its lagged version for serveral iterations, where high (>0.5) or low (<-0.5) values show a repeating pattern.

Seasonal effects

There are not enough (less than 2 periods of) data in the time series, so seasonal decomposition is not attemplted.

Linear model

And now we build a really simple linear model based on the year, the month, the day of the month and also the day of the week to predict Oil, Gold, and Stocks. The model that can be built automatically is: value ~ year + month + mday + wday.

Assumptions

In order to have reliable results, we have to check if the assumptions of the linear regression met with the data we used:

The GVLMA makes a thorough detection on the linear model, including tests generally about the fit, the shape of the distribution of the residuals (skewness and kurtosis), the linearity and the homoskedasticity. On the table we can see if our model met with the assumptions. As a generally accepted thumb-rule we use the critical p-value=0.05.

So let's see the results, which the test gave us:

The general statistic tells us about the linear model, that it does not fit to our data.

According to the GVLMA the residuals of our model's skewness does not differs significantly from the normal distribution's skewness.

The residuals of our model's kurtosis differs significantly from the normal distribution's kurtosis, based on the result of the GVLMA.

In the row of the link function we can read that the linearity assumption of our model was rejected.

At last but not least GVLMA confirms homoscedasticity.

In summary: We can 't be sure that the linear model used here fits to the data.

Linearity

As we want to fit a linear regression model, it is advisable to see if the relationship between the used variables are linear indeed. Next to the test statistic of the GVLMA it is advisable to use a graphical device as well to check that linearity. Here we will use the so-called crPlots funtion to do that, which is an abbreviation of the Component and Residual Plot.

First, we can see two lines and several circles. The red interrupted line is the best fitted linear line, which means that te square of the residuals are the least while fitting that line in the model. The green curved line is the best fitted line, which does not have to be straight, of all. The observations we investigate are the circles. We can talk about linearity if the green line did not lie too far from the red.

Predicted values

ARIMA

Here we try to identify the best ARIMA model to better understand the data or to predict future points in the series. The model is chosen according to either AIC, AICc or BIC value is:

Damn, we could not fit a model:

We are terribly sorry, but this computational intensive process
is not allowed to be run on a time-series with more then 365 values.
Please sign up for an account at rapporter.net for extra resources
or filter your data by date.

References:

Hyndman, R.J. and Khandakar, Y. (2008) "Automatic time series forecasting: The forecast package for R", Journal of Statistical Software, 26(3).